Let G be a class of graphs. The strong rainbow number of the graph H in G is the minimum number of colors k such that every graph G 2 G admits an edge coloring with at most k colors in which all copies of H are rainbow (i.e., all edges of H have different colors). In this paper, it is shown that the strong rainbow number of any 2-connected graph H in the class of outerplanar graphs is bounded from above by a constant (depending only on H).